4x-3(5x+8)<_-7 inequation

Given the inequality:
$$4 x - 3 \left(5 x + 8\right) \leq -7$$
To solve this inequality, we must first solve the corresponding equation:
$$4 x - 3 \left(5 x + 8\right) = -7$$
Solve:
Given the linear equation:

4*x-3*(5*x+8) = -7

Expand brackets in the left part

4*x-3*5*x-3*8 = -7

Looking for similar summands in the left part:

-24 - 11*x = -7

Move free summands (without x)
from left part to right part, we given:
$$- 11 x = 17$$
Divide both parts of the equation by -11

x = 17 / (-11)

$$x_{1} = - \frac{17}{11}$$
$$x_{1} = - \frac{17}{11}$$
This roots
$$x_{1} = - \frac{17}{11}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{17}{11} + - \frac{1}{10}$$
=
$$- \frac{181}{110}$$
substitute to the expression
$$4 x - 3 \left(5 x + 8\right) \leq -7$$
$$\frac{\left(-181\right) 4}{110} - 3 \left(\frac{\left(-181\right) 5}{110} + 8\right) \leq -7$$

-59       
---- <= -7
 10       

but

-59       
---- >= -7
 10       

Then
$$x \leq - \frac{17}{11}$$
no execute
the solution of our inequality is:
$$x \geq - \frac{17}{11}$$

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